DRILL

Angles * An angle is made up of two rays that share the same endpoint. To name an angle we either can use the one point where the vertex is located if there is only one angle, otherwise we must use three points making sure the vertex is in the middle. A B C

Naming Angles E D A C B

1.4 Measuring Angles & Segments

Notes(Vocab) Ruler Postulate: the distance between any two points is the absolute value of the difference.

Congruent: Is the term used in Geometry to describe two shapes or objects which are Equal.

Segment Addition Postulate: If three points A, B, and C are collinear and B is between A and C, then AB + BC =AC. A B C

Measuring Angles: an angle measure is found by taking the absolute value of the difference of each angle.

Angle Addition Postulate: If two angles share a common ray then the sum of those two angles is equal to the larger angle. B C A D

Drill Draw a segment so that A and C are the endpoints and B is somewhere between them. If AB is 10 feet and BC is 18 feet, how long is AC? If AB is 2x feet and BC is 3x + 4 feet and AC is 39 feet how long is AB?

1.5 Good Definitions

What is a Polyglob?

Properties of Good Definitions Uses clearly understood terms, meaning they should be commonly understood or previously defined. Is Precise, Avoid words such as large, sort of, and some. States what the term is, rather then what it is not. Ex: Big is the opposite of small.

Midpoint: is the point that divides a segment into two congruent parts. Perpendicular Lines: are lines that intersect to make a right angle.

Perpendicular Bisector: is a perpendicular line that passes through the mid point of a segment. Angle Bisector: is a ray that divides an angle into two congruent parts.

Drill 1) A B C If AB is 15 and AC is 80 find BC. 2) Is this a good definition? Explain An apple is a fruit that is not an orange. 3) 30, 26, 21, 15, ___, ___, ___

3) 30, 26, 21, 15, 8, 0, -9 A B C If AB is 15 and AC is 80 find BC. 80 – 15 = 65 therefore BC = 65 An apple is a fruit that is not an orange. No, b/c of the word NOT being used. 3) 30, 26, 21, 15, 8, 0, -9

1.6 Basic Constructions Objective: The students will be able to construct perpendicular bisectors and angle bisectors, as well as understand their properties.

Tools For Constructions Compass Straightedge Patty Paper Geometer’s Sketchpad

Perpendicular Bisector Is a line that is perpendicular to a segment and passes through the midpoint. Steps for Construction/Patty Paper Trace the segment on the patty paper. Label Endpoints Fold paper so that the two endpoints match up and unfold. Trace the fold to create your perpendicular bisector

Fold M B A

Steps for Construction/Patty Paper Angle Bisector Is a ray that cuts an angle into two congruent angles. Steps for Construction/Patty Paper Trace the angle on the patty paper Label Points Pinch the vertex and fold the paper so that the two rays that create the angle match up and unfold Trace the fold to create your angle bisector

C Fold E D B A

Summary Constructed Perpendicular and Angle Bisectors Found measures using both types of bisectors Creating angle bisectors will lead us into vertical angles as well as linear angles.

Drill 1) A B C If AB is 3x and BC is 2x + 10, find BC if AC equals 80 feet. 2) Does the ceiling and your desktop represent parallel planes? (WHY) 3) How many and what type of points do we need to name a plane?

1.7 Using Deductive Reasoning

Types of Angles Vertical Angles Vertical Angles are angles that are opposite each other where two lines intersect. Ex : 1 & 3 as well as 2 & 4

Types of Angles Adjacent Angles Adjacent Angles are angles that share a common endpoint and share a common ray. Ex : Angles A and B

Types of Angles Complementary Angles Two angles that have a sum of 90 degrees.

Types of Angles Supplementary Angles Two angles that have a sum of 180 degrees.

Guided Practice

Guided Practice

Guided Practice

Homework Worksheet # 1.7

1.8 The Coordinate Plane

Formulas The Distance Formula

Midpoint Formula